please solve with gams and share gams code and olsa please answer the questions at the end
Optimization of Heart Valve Production Problem Statement Biological heart valves are bioprostheses manufactured from porcine hearts for human implantation. Replacement valves needed by the human population come in different sizes. On the supply side, porcine hearts cannot be "produced to specific sizes. Moreover, the exact size of a manufactured valve cannot be determined until the biological component of pig heart has been processed. As a result, some needed sizes may be overstocked and others may be understocked. Raw hearts are provided by twelve vendors in six to eight sizes, usually in different proportions depending on how the animals are raised. The distribution of sizes in each shipment varies by the vendor, estimates for each vendor is available based on historical data as indicated in Table 1. (The numbers in the table represent the percentage of a shipment from a vendor that is of the given size, for example a shipment from vendor 1 contains 20% size 1 heart valves and no size 7 heart valves.) 4 1011 15 DE GOOD 2860.32 0. 0 002 0.01 OS 04 05 06 0.20 0.05 0.1 0.2 0.05 0.1 10,140,14 03 02 0.1 0.22 0.10.130.02 03 0.1 0.12 40.160201ODO 0,002 0,15 03 0,15 0 0.29 0.1 0.07 0 .05 0.1 0.1 0.28 0.040.16 2004 BEST OF 20.05 0.1 0. 001 000,00 002 OGOS TO GO 0. 1 00.15 Table 1: Proportion of heart valve sizes provided by each vendor Porcine specialists work with vendors to ensure distribution stability as much as possible. In this manner, the manufacturer can have a reasonably reliable estimate of the number of units of each size in each shipment. The selection of the mix of vendors and the size of their shipments is thus crucial in reducing mismatches between supply and demand. (Please note that it is not possible to mix-and-match the number of heart valves of cach size ordered from a given vendor. For example, if you order 100 heart valves from vendor 1, you predict that you will receive approximately 20 sizel valves, 30 size2 valves, etc. However, you cannot purchase only the 20 sizel valves, and leave the 30 size2 valves. You have to purchase the entire 100 valves.) The price charged for a certain size heart valve also varies by the vendor as given in Table 2. Therefore, it is also important to consider the purchase cost as the orders are made. However, it is not always possible to order from the most economical vendor because the number of heart valves that can be ordered from each vendor is limited as given in Table 3. Finally, Table 4 lists Porcine specialists work with vendors to ensure distribution stability as much as possible. In this manner, the manufacturer can have a reasonably reliable estimate of the number of units of each size in each shipment. The selection of the mix of vendors and the size of their shipments is thus crucial in reducing mismatches between supply and demand. (Please note that it is not possible to mix-and-match the number of heart valves of each size ordered from a given vendor. For example, if you order 100 heart valves from vendor 1, you predict that you will receive approximately 20 sizel valves, 30 size2 valves, etc. However, you cannot purchase only the 20 sizel valves, and leave the 30 size2 valves. You have to purchase the entire 100 valves.) The price charged for a certain size heart valve also varies by the vendor as given in Table 2. Therefore, it is also important to consider the purchase cost as the orders are made. However, it is not always possible to order from the most economical vendor because the number of heart valves that can be ordered from each vendor is limited as given in Table 3. Finally, Table 4 lists the demand for heart valves of each size to be procured from the vendors. Based on this information, the problem is to develop an LP model to determine the number of heart valves to be ordered from each vendor in order to minimize the total order cost. S120 12 0 P 10 11 12 1121121121 12212513 213.2 143 18 1414 151312 1 3313.13.2 3 14144152 16 16,1 15,8 14,8 139 148 149 14,1 14 410152 15,410,416.3 15.5 15.1 15.0 15.4 150 158 15 596416516.1 1164161 176 167 168 169 17 17 16.8 16.7 17.216.5 17 18.5 17 17.817.7 16.5 17 1117318.017SING 1 1 84 8181920, 119. 615 15 Table 2: Cost of a heart valve by size and vendor in dollars ODABODOO 10 12 1 500 500 400 500 300 500 500 400 300 500 400 500 Table 3: Heart valve availability by vendor 0278 31040020400 350 130 Table 4: Heart valve demand by size Model the above problem first in open and then in closed (algebraic) form and solve using both ExcelSolver and GAMS, (GAMS model should be in closed form and free of any embedded data.) After obtaining the optimal solution, answer the following questions based on your model. To the extent possible, do not re-solve the problem to answer the questions. Explain your answers clearly, 10236567 8 9 10 11 12 1 500 500 400 500 300 300 300 400 300 500 400 500 Table 3: Heart valve availability by vendor 11234567B 0275 310 400 320 400 350 300 130 Table 4: Heart valve demand by size Model the above problem first in open and then in closed (algebraic) form and solve using both ExcelSolver and GAMS. (GAMS model should be in closed form and free of any embedded data.) After obtaining the optimal solution, answer the following questions based on your model. To the extent possible, do not re-solve the problem to answer the questions. Explain your answers clearly. 1. Which assumptions of LP are violated in this model? 2. Suppose that the price of all heart valves sold by vendor 9 was increased by 20%. Would this impact your order policy? Explain why (not). 3. Suppose that vendor 1 is offering you a 10% discount on all heart valves that you buy. Would this impact your order policy? Explain why (not). 4. Suppose that the demand for size 3 heart valves increased from 400 to 415, what would the impact of this change be on your total cost? s. Suppose that the demand for size 6 heart valves decreased from 350 to 300, what would the impact of this change be on your total cost? 6. Suppose that the demand for size 8 heart valves decreased from 130 to 100, what would the impact of this change be on your total cost? 7. Which vendors are more important for the procurement of heart valves? If we were to eliminate some vendors to streamline our procurement efforts, which vendors should be eliminated first? 8. Which heart valve sizes are more critical in terms of the impact of changes in their demand pattern? Optimization of Heart Valve Production Problem Statement Biological heart valves are bioprostheses manufactured from porcine hearts for human implantation. Replacement valves needed by the human population come in different sizes. On the supply side, porcine hearts cannot be "produced to specific sizes. Moreover, the exact size of a manufactured valve cannot be determined until the biological component of pig heart has been processed. As a result, some needed sizes may be overstocked and others may be understocked. Raw hearts are provided by twelve vendors in six to eight sizes, usually in different proportions depending on how the animals are raised. The distribution of sizes in each shipment varies by the vendor, estimates for each vendor is available based on historical data as indicated in Table 1. (The numbers in the table represent the percentage of a shipment from a vendor that is of the given size, for example a shipment from vendor 1 contains 20% size 1 heart valves and no size 7 heart valves.) 4 1011 15 DE GOOD 2860.32 0. 0 002 0.01 OS 04 05 06 0.20 0.05 0.1 0.2 0.05 0.1 10,140,14 03 02 0.1 0.22 0.10.130.02 03 0.1 0.12 40.160201ODO 0,002 0,15 03 0,15 0 0.29 0.1 0.07 0 .05 0.1 0.1 0.28 0.040.16 2004 BEST OF 20.05 0.1 0. 001 000,00 002 OGOS TO GO 0. 1 00.15 Table 1: Proportion of heart valve sizes provided by each vendor Porcine specialists work with vendors to ensure distribution stability as much as possible. In this manner, the manufacturer can have a reasonably reliable estimate of the number of units of each size in each shipment. The selection of the mix of vendors and the size of their shipments is thus crucial in reducing mismatches between supply and demand. (Please note that it is not possible to mix-and-match the number of heart valves of cach size ordered from a given vendor. For example, if you order 100 heart valves from vendor 1, you predict that you will receive approximately 20 sizel valves, 30 size2 valves, etc. However, you cannot purchase only the 20 sizel valves, and leave the 30 size2 valves. You have to purchase the entire 100 valves.) The price charged for a certain size heart valve also varies by the vendor as given in Table 2. Therefore, it is also important to consider the purchase cost as the orders are made. However, it is not always possible to order from the most economical vendor because the number of heart valves that can be ordered from each vendor is limited as given in Table 3. Finally, Table 4 lists Porcine specialists work with vendors to ensure distribution stability as much as possible. In this manner, the manufacturer can have a reasonably reliable estimate of the number of units of each size in each shipment. The selection of the mix of vendors and the size of their shipments is thus crucial in reducing mismatches between supply and demand. (Please note that it is not possible to mix-and-match the number of heart valves of each size ordered from a given vendor. For example, if you order 100 heart valves from vendor 1, you predict that you will receive approximately 20 sizel valves, 30 size2 valves, etc. However, you cannot purchase only the 20 sizel valves, and leave the 30 size2 valves. You have to purchase the entire 100 valves.) The price charged for a certain size heart valve also varies by the vendor as given in Table 2. Therefore, it is also important to consider the purchase cost as the orders are made. However, it is not always possible to order from the most economical vendor because the number of heart valves that can be ordered from each vendor is limited as given in Table 3. Finally, Table 4 lists the demand for heart valves of each size to be procured from the vendors. Based on this information, the problem is to develop an LP model to determine the number of heart valves to be ordered from each vendor in order to minimize the total order cost. S120 12 0 P 10 11 12 1121121121 12212513 213.2 143 18 1414 151312 1 3313.13.2 3 14144152 16 16,1 15,8 14,8 139 148 149 14,1 14 410152 15,410,416.3 15.5 15.1 15.0 15.4 150 158 15 596416516.1 1164161 176 167 168 169 17 17 16.8 16.7 17.216.5 17 18.5 17 17.817.7 16.5 17 1117318.017SING 1 1 84 8181920, 119. 615 15 Table 2: Cost of a heart valve by size and vendor in dollars ODABODOO 10 12 1 500 500 400 500 300 500 500 400 300 500 400 500 Table 3: Heart valve availability by vendor 0278 31040020400 350 130 Table 4: Heart valve demand by size Model the above problem first in open and then in closed (algebraic) form and solve using both ExcelSolver and GAMS, (GAMS model should be in closed form and free of any embedded data.) After obtaining the optimal solution, answer the following questions based on your model. To the extent possible, do not re-solve the problem to answer the questions. Explain your answers clearly, 10236567 8 9 10 11 12 1 500 500 400 500 300 300 300 400 300 500 400 500 Table 3: Heart valve availability by vendor 11234567B 0275 310 400 320 400 350 300 130 Table 4: Heart valve demand by size Model the above problem first in open and then in closed (algebraic) form and solve using both ExcelSolver and GAMS. (GAMS model should be in closed form and free of any embedded data.) After obtaining the optimal solution, answer the following questions based on your model. To the extent possible, do not re-solve the problem to answer the questions. Explain your answers clearly. 1. Which assumptions of LP are violated in this model? 2. Suppose that the price of all heart valves sold by vendor 9 was increased by 20%. Would this impact your order policy? Explain why (not). 3. Suppose that vendor 1 is offering you a 10% discount on all heart valves that you buy. Would this impact your order policy? Explain why (not). 4. Suppose that the demand for size 3 heart valves increased from 400 to 415, what would the impact of this change be on your total cost? s. Suppose that the demand for size 6 heart valves decreased from 350 to 300, what would the impact of this change be on your total cost? 6. Suppose that the demand for size 8 heart valves decreased from 130 to 100, what would the impact of this change be on your total cost? 7. Which vendors are more important for the procurement of heart valves? If we were to eliminate some vendors to streamline our procurement efforts, which vendors should be eliminated first? 8. Which heart valve sizes are more critical in terms of the impact of changes in their demand pattern
